(1) seems pretty common, and from what I know of Mr Sailer, I imagine it underlies most of his examples- there'll be an article highlighting some inequality or problem and the "facts which undermine the premises of the piece" are the suggested causes, the "joke" is that the author's see the outcome as undesirable while Sailer sees attempts to change the outcome as foolish.

Conspicuous wrongness sounds close to belief as attire (the article with the pagan lady who believed something she obviously didn't think was true) but with the addition that someone believes it's true, so the motive is not to disagree with them. I think ideologues often identify each other by the viewpoints they can be certain nobody else shares- how else to explain why the unreadable Atlas Shrugs remains more popular than Rand's other books, which are no less strident but considerably more appealing to outsiders.